In recent months, Ryanair has angered passengers who wish to travel together by suggesting that they must pay an additional charge in order to sit next to each other on a flight.

In the past, if a party were to make a combined booking, it was highly likely that they would be sitting together. This seems to have changed in recent months with seat allocation appearing to be totally random.

Ryanair has denied that its seating policy has changed and said that it is not trying to split groups up but this has been questioned by Jennifer Rogers, the director of statistical consultancy at Oxford University.

When asked by the consumer program, Watchdog, to calculate the probability of four researchers being randomly allocated middle seats on all four flights, she calculated the probability to be 1:543,094,880 – ten times less likely that the probability of a UK National Lottery win at 1:45,057,474.

On the Manchester to Dublin flight, Rogers noticed that there were 65 seats available at the time of check in. 15 of those seats were in the middle.

“Therefore,” she said, “we can calculate the probability of being allocated four middle seats on this flight as 1 in 500. Carrying out similar calculations for the other flights, and then combining these probabilities together, I was able to calculate the probability of four researchers being allocated middle seats on their four flights, if the seating allocation was indeed random, as 1:543,094,880. A tiny probability.”

When put to Kenny Jacobs, Ryanair’s chief marketing officer, he argued that, “this claim isn’t true. When a customer does not purchase a seat, they are randomly allocated a seat. The algorithm changes on each flight and each route by reference to demands for reserved seats.”

“Some random seat passengers are confused by the appearance of empty seats beside them when they check-in up to four days prior to departure,” he argued. “The reason they can’t have these window or aisle seats is that these are more likely to be selected by reserved seat passengers many of whom only check-in 24 hours prior to departure. Since our current load factor is 97 per cent, we have to keep these window and aisle seats free to facilitate those customers who are willing to pay (from £2) for them.”

According to Rogers, “I don’t think they do allocate seats randomly. Ryanair have said that they save the window and aisle seats. I think the rows will be randomly allocated, but you will be given a middle seat and then they fill up from there.”